1. Terry Turner, Lecturer School of Mathematical and Statistical Sciences Arizona State University

2. 1. 1. The domain is constrained to a closed and bounded region most of the time. Closed and bounded regions are guaranteed to have absolute extremes. 2. 2. We analyze the partial derivatives for extremes within the region. 3. 3. We analyze all paths for extremes. 4. 4. We identify all corner points. 5. 5. We evaluate everything we found. a) a) The max is the highest z-value; b) b) The min is the lowest z-value; c) c) Discard anything in between.

4. Maximize: Subject to:

5. Find the maximum and minimum values for Subject to: 0

6. A CEO invests some of his $120,000 savings in an account paying 5% annual interest and the rest in another account paying 6% annual interest. 1. 1. He invests at least $60,000 in the account paying 6%. 2. 2. The amount in the 6% account must be no more than three times the amount in the 5% account. How much must he invest in each account to maximize interest at the end of the year?

7. Terry Turner, Lecturer School of Mathematical and Statistical Sciences Arizona State University